Non-Archimedean Mathematics and the formalism of Quantum Mechanics

Publication date: 11 September 2018

Abstract: This paper is divided in four parts. In the introduction, we discuss the program and the motivations of this paper. In section 2, we introduce the non-Archimedean field of Euclidean numbers E and we present a summary of the theory of {Lambda}-limits which can be considered as a different approach to nonstandard methods. In the third part (section 3), we define axiomatically the space of ultrafunctions which are a kind of generalized function based on the field of Euclidean numbers E. Finally, we describe an application of the previus theory to the formalism of classical Quantum Mecanics.

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